MA 5330 Real Analysis
Real number system and its order completeness, sequences and series of real numbers. Metric spaces: Basic concepts, continuous functions, completeness, Baire Category Theorem, Contraction mapping theorem, connectedness, Intermediate Value Theorem, Compactness, Heine-Borel Theorem. Differentiation, Taylor's theorem, Riemann-Stieltjes integral and its properties, Improper integrals. Sequences and series of functions, Uniform convergence, power series and Fourier series, Weierstrass approximation theorem, Equicontinuity, Arzela-Ascoli theorem.
1. W. Rudin, Principles of Mathematical Analysis, Mc-Graw Hill, 1976.
2. C. C. Pugh, Real Mathematical Analysis, Springer, 2002.
1 T. M. Apostol, Mathematical Analysis, Addison-Wesley, 1974.
2. G. F. Simmons, Topology and Modern Analysis, Kreiger, 2003.